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JOURNALS // Trudy Moskovskogo Matematicheskogo Obshchestva
Tr. Mosk. Mat. Obs., 2022, Volume 83, Issue 1, Pages 181–217 (Mi mmo670)
On a class of degenerate hypoelliptic polynomials
H. G. Kazaryan, V. N. Margaryan

References
1. V. I. Burenkov, “Analog teoremy Khermandera o gipoelliptichnosti dlya funktsii, stremyaschikhsya k nulyu na beskonechnosti”, Sb. dokladov VII sovetsko-chekhoslovatskogo seminara, Izd-vo Erevan. un-ta, Erevan, 1982, 63–67
2. L. R. Volevich, S. G. Gindikin, “Ob odnom klasse gipoellipticheskikh polinomov”, Matem. sb., 75(117):3 (1968), 400–416  mathnet  zmath
3. O. R. Gabrielyan, “O stepeni prevalirovaniya vypozhdayuschikhsya mnogochlenov i ob ikh gipoelliptichnosti”, Izv. NAN Armenii. Matematika, XXXVIII:6 (2003), 63–82  zmath
4. E. A. Gorin, “Ob asimptoticheskikh svoistvakh mnogochlenov i algebraicheskikh funktsii ot neskolkikh peremennykh”, UMN, 16:1 (1961), 91–118  mathnet  mathscinet  zmath
5. S. G. Gindikin, “Energeticheskie otsenki, svyazannye s mnogogrannikom Nyutona”, Tr. MMO, 31, 1974, 189–236  mathnet  zmath
6. V. V. Grushin, “Ob odnom klasse gipoellipticheskikh operatorov”, Matem. sb., 83:3 (1970), 456–473  mathnet  mathscinet  zmath
7. G. G. Kazaryan, “Otsenki $L_{p}$" norm proizvodnykh funktsii cherez nabora neregulyarnykh differentsialnykh operatorov”, Diff. uravneniya, 5:5 (1969), 911–921  mathnet  zmath
8. G. G. Kazaryan, “Ob odnom semeistve gipoellipticheskikh polinomov”, Izv. AN Arm. SSR. Matematika, IX:3 (1974), 189–211  zmath
9. G. G. Kazaryan, “O dobavlenii mladshikh chlenov k differentsialnym polinomam”, Izv. AN Arm. SSR. Matematika, IX:6 (1974), 473–485
10. G. G. Kazaryan, “O sravnenii differentsialnykh operatorov i differentsialnykh operatorakh postoyannoi sily”, Tr. MIAN, 131, 1974, 94–118  mathnet  zmath
11. G. G. Kazaryan, “Otsenki differentsialnykh operatorov i gipoellipticheskie operatory”, Tr. MIAN, 140, 1976, 130–161  mathnet  zmath
12. G. G. Kazaryan, “Operatory postoyannoi sily s otsenkoi snizu cherez proizvodnye i formalno gipoellipticheskie operatory”, Anal. Math., 3:4 (1977), 263–289  crossref  mathscinet  zmath
13. G. G. Kazaryan, “Sravnenie moschnosti mnogochlenov i ikh gipoelliptichnost”, Tr. MIAN, 150, 1979, 143–159  mathnet  zmath
14. G. G. Kazaryan, “O pochti gipoellipticheskikh mnogochlenakh, vozrastayuschikh na beskonechnosti”, Izv. NAN Armenii. Matematika, 46:6 (2011), 11–30  mathscinet  zmath
15. G. G. Kazaryan, V. N. Markaryan, “Kriterii gipoelliptichnosti v terminakh moschnosti i sily operatorov”, Tr. MIAN, 150, 1979, 128–142  mathnet  zmath
16. G. G. Kazaryan, V. N. Margaryan, “Nositel gipoelliptichnosti lineinykh differentsialnykh operatorov”, Izv. NAN Armenii. Matematika, XXI:5 (1986), 453–470  mathscinet
17. G. G. Kazaryan, V. N. Margaryan, “Kriterii gipoelliptichnosti mnogochlenov v terminakh Zaidenberga"– Tarskogo”, Izv. NAN Armenii. Matematika, XLI:3 (2006), 38–55
18. V. N. Markaryan, “Dobavlenie mladshikh chlenov, sokhranyayuschikh gipoelliptichnost operatora”, Izv. NAN Armenii. Matematika, XV:6 (1980), 443–460  zmath
19. V. P. Mikhailov, “O povedenii na beskonechnosti odnogo klassa mnogochlenov”, Tr. MIAN, 19, 1967, 59–80  mathnet
20. S. M. Nikolskii, “Pervaya kraevaya zadacha dlya odnogo obschego lineinogo uravneniya”, DAN SSSR, 146:4 (1962), 767–769  mathnet  zmath
21. L. Khermander, Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, V 4-kh t., v. 2, Mir, M., 1986
22. F. Bouchut, “Hypoelliptic regularity in kinetic equations”, J. Math. Pures Appl., 81:11 (2002), 1135–1159  crossref  mathscinet  zmath
23. L. Cattabriga, “Su una classe di polinomi ipoellittici”, Rend. Sem. Mat. Univ. Padova, 36 (1966), 285–309  mathscinet  zmath
24. L. Cattabriga, “Uno spazio funzionale connesso ad una classe di operatori ipoellittici”, Symposia Mathematica, VII, Acad. Press, London, 1971, 547–558  mathscinet
25. M. Chaleyat-Maurel, “La condition d'hypoellipti{c}ité d'Hörmander”, Astérisque, 84–85 (1981), 189–202  zmath
26. J. Friberg, “Multi-quasielliptic polynomials”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3), 21 (1967), 239–260  mathscinet  zmath
27. “L. Gårding, B. Malgrange”, Math. Scand., 9 (1961), 5–21  crossref  mathscinet  zmath
28. H. G. Ghazaryan, V. N. Margaryan, “On increase at infinity of almost hypoelliptic polynomials”, Eurasian Math. J., 4:4 (2013), 30–42  mathnet  mathscinet  zmath
29. S. G. Gindikin, L. R. Volevich, The method of Newton's polyhedron in the theory of partial differential equations, MASS, 86, Kluwer Academic Publishers Group, Dordrecht, 1992  mathscinet
30. L. Hörmander, The analysis of linear partial differential operators, v. I, Springer-Verlag, Berlin, 1983  mathscinet
31. A. G. Khovanskii, “Newton Polyhedra (algebra and geometry)”, AMS Transl. (2), 153 (1992), 1–15
32. P. K. Kythe, Fundamental solutions for differential operators and applications, Birkhäuser Boston, Boston, MA, 1996  mathscinet  zmath
33. B. Malgrange, “Sur une classe d'opérateurs différentiels hypoelliptiques”, Bull. Math. France., 85:3 (1957), 283–306  crossref  mathscinet  zmath
34. E. Pehkonen, Regularität der schwachen Lösungen linearer quasielliptischer Dirichletprobleme, PhD Thesis, Matematiikan Laitos Berichte, 16, Univ. Jyväskylä, 1976  mathscinet
35. E. Pehkonen, “Ein hypoelliptisches Dirichletproblem”, Soc. Sci. Fenn. Comment. Phys.-Math., 48:3 (1978), 131–143  mathscinet  zmath
36. B. Pini, “Osservazioni sulla ipoellittisità”, Boll. Un. Mat. Ital. (3), 18:4 (1963), 420–432  mathscinet  zmath
37. B. Pini, “Sulla classe di Gevrey delle soluzioni di certe equazioni ipoellittiche”, Boll. Un. Mat. Ital. (3), 18:3 (1963), 260–269  mathscinet  zmath
38. F. Trèves, “Opérateurs différentiels hypoelliptiques”, Ann. Inst. Fourier (Grenoble), 9 (1959), 1–73  crossref  mathscinet  zmath
39. C. Zuily, “Sur l'hypoellipticité des opérateurs différentiels du second ordre à coefficients réels”, J. Math. Pures Appl., 55:1 (1976), 99–129  mathscinet  zmath

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